There are statues that you can unlock. They appear right next to your base around the tree. The statues are based on new 4th generation pokemon that little info was known about around the time of this games release.

Bonsly
This statue can be unlocked by defeating all the mini Dungeons in the Makuhita Dojo.

Lucario
This statue can be unlocked by getting 15000 rescue points. You also get the Lucario rank.

Weavile
This statue can be unlocked by finishing Purity Forest, and Joyous Tower.

Mime Jr.
This statue can be unlocked by finsihing Purity Forest, or Joyous Tower.